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Piezoelectric-based energy harvesting devices provide an attractive approach to powering remote devices as ambient mechanical energy from vibrations is converted to electrical energy. These devices have numerous potential applications, including actuation, sensing, structural health monitoring, and vibration control -- the latter of which is of particular interest here. This work seeks to develop an understanding of energy harvesting behavior within the framework of a semi-active technique for reducing turbomachinery blade vibrations, namely resonance frequency detuning. In contrast with the bulk of energy harvesting research, this effort is not focused on maximizing the power output of the system, but rather providing the low power levels required by resonance frequency detuning. The demands of this technique dictate that harvesting conditions will be far from optimal, requiring that many common assumptions in conventional energy harvesting research be relaxed. Resonance frequency detuning has been proposed as a result of recent advances in turbomachinery blade design that have, while improving their overall efficiency, led to significantly reduced damping and thus large vibratory stresses. This technique uses piezoelectric materials to control the stiffness, and thus resonance frequency, of a blade as the excitation frequency sweeps through resonance. By detuning a structure*s resonance frequency from that of the excitation, the overall peak response can be reduced, delaying high cycle fatigue and extending the lifetime of a blade. Additional benefits include reduced weight, drag, and noise levels as reduced vibratory stresses allow for increasingly light blade construction. As resonance frequency detuning is most effective when the stiffness states are well separated, it is necessary to harvested at nominally open- and short-circuit states, corresponding to the largest separation in stiffness states. This presents a problem from a harvesting standpoint however, as open- and short-circuit correspond to zero charge displacement and zero voltage, respectively, and thus there is no energy flow. It is, then, desirable to operate as near these conditions as possible while still harvesting sufficient energy to provide the power for state-switching. In this research a metric is developed to study the relationship between harvested power and structural stiffness, and a key result is that appreciable energy can be harvested far from the usual optimal conditions in a typical energy harvesting approach. Indeed, sufficient energy is available to power the on-blade control while essentially maintaining the desired stiffness states for detuning. Furthermore, it is shown that the optimal switch in the control law for resonance frequency detuning may be triggered by a threshold harvested power, requiring minimal on-blade processing. This is an attractive idea for implementing a vibration control system on-blade, as size limitations encourage removing the need for additional sensing and signal processing hardware.

This research thesis aims to achieve the structural analysis and active vibration damping of the Tetraform machining structure. The Tetraform is a space frame made up of four equilateral triangles with spherical masses at the four vertices. This frame was originally developed for grinding of optical lenses and is now being adapted for use in micro-precision milling. The Tetraform is beneficial to the milling process due to its exceptionally high dynamic stiffness characteristics, which increases the machining stability and allows for higher material removal rates and accuracy. However, there are still some modes of vibration that are critical to the milling process and need to be dampened out. Under operating conditions of many structures, resonant modes of vibration can easily be excited which often lead to structural failure or significant reduction in operating performance. For the milling application, resonant frequencies of the machining structure can severely limit the milling process. The goal of the presented research is to increase surface and subsurface integrity with optimal material removal rate and least possible machining vibration, while maintaining accurate precision and surface finish. The vibrations from the machine tool not only affect the quality of the machined part but also the machine tool itself, since the cutting tool is susceptible to break or wear quickly when operating at high vibration modes, thus inevitably decreasing tool life. Vibration control has gained considerable attention in many areas including aerospace, automotive, structural, and manufacturing. Positive Position Feedback (PPF) is a vibration control scheme that is commonly used for its robust stability properties. A PPF controller works as a low pass filter, eliminating instability from unmodeled higher-frequency modes. The PPF controller concept is used in developing an active vibration control scheme to target the critical frequencies of the Tetraform. The controller is implemented with use of piezoelectric actuators and sensors, where the sensors are bonded to the opposing sides of the beams as the actuators, allowing for the assumption of collocation. The sensor/actuator pairs are placed at an optimal location on the Tetraform with high modal displacements for all the critical frequencies. Multiple finite element models are developed in order to analyze the structural dynamics and allow for controller design. A model is developed in the finite element software ANSYS and is used to obtain the Tetraform's dynamic characteristics, which include natural frequencies and mode shapes. This model is also used to visualize the changes in mode shapes due to structural modifications or different material selections. Other models are also developed in Matlab and Simulink. This consists of the creation of a finite element model which is then converted to state space. The piezoelectric transducers are included in this model for the input and output of the state space model. This model can be used for controller design where the goal is to create maximum decibel reduction at critical frequencies while attempting to minimize controller effort.

In this work passive piezoelectric devices for vibration damping are studied. It is developed the basic idea of synthesizing electrical wave guides to obtain an optimal electro-mechanical energy exchange and therefore to dissipate the mechanical vibrational energy in the electric form. Modular PiezoElectroMechanical (PEM) structures are constituted by continuous elastic beams (or bars) coupled, by means of an array of PZT transducers, to lumped dissipative electric networks. Both refined and homogenized models of those periodic systems are derived by an energetic approach based on the principle of virtual powers. Weak and strong formulation of the dynamical problem are presented having in mind future studies involving the determination of numerical solutions. In this framework the effectiveness of the proposed devices for the suppression of mechanical vibrations is investigated by a wave approach, considering both the extensional and flexural oscillations. The optimal values of the electric parameters for a fixed network topology are derived analytically by a pole placement technique. Their sensitivities on the dimensions of the basic cell of the periodic system and on the design frequency are studied. Moreover the dependence of damping performances on the frequency is analyzed. Comparing the performances of different network topological configurations, the advantages of controlling a mechanical structure with an electric analog are shown. As a consequence of those results, new interconnections of PZT transducers are proposed. An experimental setup for the validation of the analytical and numerical results is proposed and tested. A classical experience on resonant shunted PZT is reproduced. Future experimental work is programmed. / Master of Science

The aim of this thesis is to show that it is possible to damp mechanical vibrations in a given frame, constituted by Euler beam governed by the equations of an elastica, by means of piezoelectric actuators glued on every beam and interconnected each other via electrical networks.Since we believe that the most efficient way to damp mechanical vibrations by means of electrical networks, is to realize a strong modal coupling between the electrical and the mechanical motion, we will synthesize a distributed circuit analog to the Euler beam.We will approach this synthesis problem following the black box approach to mechanical systems, studied by many engineers and scientists during the 1940's in an attempt to design analog computers.It will be shown that it is possible to obtain a quick energy exchange between its mechanical and electrical forms, using available piezoelectric actuators.Finally we will study a numerical simulation for the damping of transverse vibrations of a beam clamped at both ends. / Master of Science

No / Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorithm so as to exploit special features of the hardware and avoid associated architecture shortcomings. This paper presents an investigation into the analysis and design mechanisms that will lead to reduction in the execution time in implementing real-time control algorithms. The proposed mechanisms are exemplified by means of one algorithm, which demonstrates their applicability to real-time applications. An active vibration control (AVC) algorithm for a flexible beam system simulated using the finite difference (FD) method is considered to demonstrate the effectiveness of the proposed methods. A comparative performance evaluation of the proposed design mechanisms is presented and discussed through a set of experiments.

Yes / This correspondence presents an investigation into the comparative performance of an active vibration control (AVC) system using a number of intelligent learning algorithms. Recursive least square (RLS), evolutionary genetic algorithms (GAs), general regression neural network (GRNN), and adaptive neuro-fuzzy inference system (ANFIS) algorithms are proposed to develop the mechanisms of an AVC system. The controller is designed on the basis of optimal vibration suppression using a plant model. A simulation platform of a flexible beam system in transverse vibration using a finite difference method is considered to demonstrate the capabilities of the AVC system using RLS, GAs, GRNN, and ANFIS. The simulation model of the AVC system is implemented, tested, and its performance is assessed for the system identification models using the proposed algorithms. Finally, a comparative performance of the algorithms in implementing the model of the AVC system is presented and discussed through a set of experiments.

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